For the toad-in-the-hole, place the plain flour into a bowl and make a well in the centre. Whisk in the eggs and milk to make a smooth batter. Place in the fridge overnight.
The next day, when you're ready to cook the toad-in-the-hole, preheat the oven to 220C/425F/Gas 7.
Heat the olive oil in a frying pan, add the sausages and cook, turning frequently, until browned on all sides.
Place the beef dripping into a roasting tin and place in the oven. Remove the batter from the fridge and whisk lightly until smooth and combined - it may have separated slightly overnight. Add the thyme leaves and season with salt and freshly ground black pepper.
Remove the roasting tin from the oven, add the sausages and pour over the batter. Transfer to the oven and bake for 35-40 minutes, then open the oven door to remove the steam. Lower the oven temperature to 180C/350F/Gas 4 and cook for a further ten minutes, until golden-brown. Remove from the oven and leave to stand for a few minutes.
For the gravy, heat most of the butter in a pan, add the onions and cook for ten minutes, or until soft.
Add the gravy granules and yeast extract and stir to combine. Add the vegetable stock and bring to the boil. Reduce the heat and simmer for five minutes until thickened. Season with salt and freshly ground black pepper and stir in the remaining knob of butter.
To serve, place portions of the toad-in-the-hole onto serving plates and pour over the gravy.